Wave division multiplexing (WDM) optical networks are well known in the art. A WDM channel is typically transmitted by a single mode semiconductor laser. Information to be communicated is imposed on the light by modulating the laser current or by externally modulating the light by applying a voltage to a modulator coupled to the laser source. A receiver employs a photo-detector that converts the light into electric current. Typically, there are two employed methodologies for detecting the received light: direct detection and coherent detection.
Due to the rapid growth of optical networks and the need for greater capacity, significant research has focused on finding efficient multi-level optical modulation formats. Any digital modulation scheme uses a finite number of distinct signals to represent digital data. Phase-shift-keying (PSK) uses a finite number of phases, each assigned a unique pattern of binary bits. Usually, each phase encodes an equal number of bits, and each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thereby recovering the original data. The receiver compares the phase of the received signal to a reference signal. This expedient utilizes coherent detection and is referred to as CPSK.
BPSK (also sometimes called PRK, Phase Reversal Keying) is the simplest form of PSK. It utilizes a pair of phases separated by 180° and is known as 2-PSK. Quaternary or quadriphase PSK, 4-PSK, or 4-QAM (QPSK) uses four points on a constellation diagram as is known in the art. The four-phase QPSK can encode two bits per symbol—twice the rate of BPSK—and experimentation has demonstrated that this may double the data rate compared to a BPSK system while maintaining the bandwidth of the signal. Alternatively, QPSK can maintain the data-rate of BPSK at half the requisite bandwidth.
Optical modulations based on four-level quadrature-phase-shift-key (QPSK) have been effectively demonstrated for both 40 Gb/s and 100 Gb/s optical transmission. In the quest for even higher spectral efficiency, eight-level 8-PSK modulation has been proposed and demonstrated experimentally.
8-QAM is another eight-level modulation format. In comparison to 8-PSK, 8-QAM is tolerant of greater noise (on the order of 1.6 dB), with identical spectral utilization. Now, even 16-QAM expedients are being developed and introduced.
In all of these systems, the modulated signal is typically detected either via direct or coherent detection, where a photo-detector receives the modulated optical signal and converts the same to an electrical signal representative of the optical power, or where a discriminator is utilized prior to the photo-detector to convert the phase changes into power values that the photo-detector can detect, respectively.
Coherent detection treats optical signals in a manner analogous to RF, with response to the amplitude and phase of each wavelength. In coherent detection, an incoming optical signal is mixed with light from a local oscillator source. When the combined signals are detected by a photo-detector, the photocurrent contains a component at a frequency that is the difference between the signal frequency and the local oscillator frequency. This difference is known as an intermediate frequency and contains all the information (amplitude and phase) carried by the optical signal. Since the new carrier frequency is much lower, all information can be recovered using typical radio demodulation methodology. Coherent receivers only see signals that are close in wavelength to the local oscillator and thus by tuning the local oscillator's wavelength, a coherent receiver operates in a manner analogous to a tunable filter. Homodyne detection produces a photocurrent that is passed to a decision circuit that outputs the unambiguous “1” or “0” values. Heterodyne detection requires that the photocurrent be processed by a demodulator to recover the information from the intermediate frequency. Balanced detection replaces a 2:1 combiner with a 2:2 combiner, where each of the outputs are detected and the difference then taken by a subtracting component.
The aforementioned PDM modulation formats utilize a constant modulus algorithm (CMA) for blind polarization recovery, polarization-mode dispersion (PMD) and residual chromatic dispersion (CD) compensation as described by D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems”, IEEE Trans. Communications, Vol. Com-28, Nov. 11, 1980, pp. 1867-1875, which is incorporated by reference herein. More advanced modulation formats such as PDM-8QAM (quadrature-amplitude modulation) and PDM-16QAM have also been explored theoretically for high-speed and high-spectral efficiency transmission as disclosed in Joseph M. Kahn and Keang-Po Ho, “Spectral Efficiency Limits and Modulation/Detection Techniques for DWDM Systems”, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 10, No. 2, March/April 2004, pp. 259-272, which is incorporated by reference herein. For a PDM-M-QAM signal, however, the traditional CMA blind equalization algorithm is not effective for polarization de-multiplexing and PMD compensation. The is because such modulation formats do not present constant symbol amplitude, and therefore the error signals calculated by using the CMA will not approach zero, even with the ideal signal. Non-zero error signals not only leads to extra noise after equalization, but also cause a problem with local minima. Therefore a better equalization algorithm is required for such advanced modulation formats.